Professor Mueller teaches two graduate seminars--the proseminar on American Politics and the seminar on Congress and the Presidency. At the undergraduate level, she teaches Women and Politics, the Presidency, Interest Groups and Lobbying, Environmental Politics and Policy, Introduction to Political Science Research, and the Political Science capstone. She regularly directs undergraduate and graduate independent studies and theses in the area of congressional politics, public policy, interest groups, and women and politics.

Professor Mueller primarily conducts research on gender and politics, focusing on questions of descriptive and substantive policy representation. Her publications include a book chapter on "soccer moms" and voting, in Engaging the Public: How the Government and Media Can Reinvigorate American Democracy and a forthcoming chapter on gender, campaigning and Twitter, in Social Media and Politics, co-authored with students. She has a chapter on Teddy Roosevelt's rhetoric and conservationism in From the Bully Pulpit: Presidential Rhetoric, Speeches, and the Shaping of Public Policy. She has also published in PS: Political Science & Politics, The Thomas Jefferson Law Review, The U.S. Government and the Environment, and Managing Environmental Policies: A Casebook.